Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C67 · Schur multiplier (H2) = C24 |
| direct product | C67×#18077 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C67 | C22×D4 |
| commutator | C2×C4 | C23×C4×C67 |
| Frattini, cosocle | C42 | C24×C67 |
| socle | C22×C67 | C2×C4×D4 |
| prime radical | #121×C67 | C2×C4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C67 ◁ C4×M16×C67 ◁ G | |
588 conjugacy classes of subgroups.
| minimal degree | μ(G) = 99 |
| transitive degree | μt(G) = 8576 |
A minimal faithful permutation representation — 4 generators on 99 points:
(1,2)(3,9)(4,12)(5,7)(6,10)(8,14)(11,16)(13,15)(17,18,22,25,23,19,21,27)(20,24,30,31,28,26,29,32)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99);(1,3,5,11)(2,6,7,15)(4,13,14,10)(8,16,12,9)(17,19,23,18)(20,26,28,24)(21,25,22,27)(29,31,30,32);(17,20,22,30,23,28,21,29)(18,24,25,31,19,26,27,32);(2,7)(6,15)(8,12)(9,16)(18,19)(20,28)(25,27)(29,30)3886 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 11065);